Wavelet Analysis of Multivariate Spatio-Temporal Data and Its Application to US Rain Fall Data

Abstract

In this talk we propose a method of wavelet analysis for multivariate spatio-temporal data, which are observed at irregularly spaced stations in discrete time, when the spatial covariances are spatially dependent. By a reinterpretation of Whittle likelihood function for stationary time series, we extend a frequency domain expression for time series to that for spatial data via modified Haar wavelets and try a multivariate extension by coregionalization. We propose an estimation method for the parameters by a spatio-temporal extension of Whittle likelihood estimation for time series, which opens a way of computing likelihood functions for huge data sets comprised of more than several hundred thousand space time points. We demonstrate the proposed modelling for US precipitation data in June, July and August from 1987 to 1997, which shows that the wavelet model has smaller mean square errors of kriging and forecasting than some benchmarks by a kernel smoothing. ?